cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 18 results. Next

A133529 Sum of squares of three consecutive primes.

Original entry on oeis.org

38, 83, 195, 339, 579, 819, 1179, 1731, 2331, 3171, 4011, 4899, 5739, 6867, 8499, 10011, 11691, 13251, 14859, 16611, 18459, 21051, 24219, 27531, 30219, 32259, 33939, 36099, 40779, 46059, 52059, 55251, 60291, 64323, 69651, 74019, 79107, 84387, 89859, 94731, 101283
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Comments

It is easy to see that all terms > 83 are divisible by 3.
Likewise all terms except 38 are congruent to 3 (mod 8). - Franklin T. Adams-Watters, Jun 17 2015

Examples

			a(1)=38 because 2^2 + 3^2 + 5^2 = 38.

Links

Crossrefs

Cf. A034963, A133524-A133528, A133530-A133533.

Programs

  • Magma
    [&+[ NthPrime(n+i)^2 :  i in [0..2]] : n in [1..20]]; // K. D. Bajpai, Jun 17 2015
  • Mathematica
    a = 2; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[50]]^2, 3, 1] (* Vincenzo Librandi, Jun 18 2015 *)
  • PARI
    for( n= 1, 100,  k= sum(i=n, n+2, prime(i)^2) ; print1(k, ", ")) \\ K. D. Bajpai, Jun 17 2015

Formula

a(n) = A069484(n) + A001248(n+2). - Michel Marcus, Nov 08 2013

Extensions

a(38)-a(41) from K. D. Bajpai, Jun 18 2015

A133526 Sum of fourth powers of four consecutive primes.

Original entry on oeis.org

3123, 17748, 46228, 129124, 257044, 522244, 1200964, 2040964, 3784804, 6330724, 9042244, 12998404, 19014724, 28306324, 38733364, 54004804, 71526004, 87806884, 112911124, 140218324, 177548884, 237679924, 302790244, 367882804, 436220164
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=3123 because 2^4+3^4+5^4+7^4=3123.

Links

Crossrefs

Cf. A034963, A133524, A133525, A133527, A133528.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[30]]^4,4,1] (* Harvey P. Dale, Sep 09 2014 *)
  • PARI
    a(n)=sum(i=n,n+3,prime(i)^4) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = A133531(n) + A030514(n+3). - Michel Marcus, Nov 08 2013
a(n) ~ 4n^4 log^4 n. - Charles R Greathouse IV, Apr 29 2015

A133530 Sum of third powers of three consecutive primes.

Original entry on oeis.org

160, 495, 1799, 3871, 8441, 13969, 23939, 43415, 66347, 104833, 149365, 199081, 252251, 332207, 458079, 581237, 733123, 885655, 1047691, 1239967, 1453843, 1769795, 2189429, 2647943, 3035701, 3348071, 3612799, 3962969, 4786309
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=160 because 2^3+3^3+5^3=160.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133531, A133532, A133533.

Programs

  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133534(n) + A030078(n+2). - Michel Marcus, Nov 08 2013

A133525 Sum of third powers of four consecutive primes.

Original entry on oeis.org

503, 1826, 3996, 8784, 15300, 26136, 48328, 73206, 117000, 173754, 228872, 302904, 401128, 537586, 685060, 882000, 1091034, 1274672, 1540730, 1811754, 2158812, 2682468, 3219730, 3740670, 4260744, 4643100, 5055696, 6011352, 7034400
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=503 because 2^3+3^3+5^3+7^3=503.

Links

Crossrefs

Cf. A034963, A133524, A133526, A133527, A133528.

Programs

  • Maple
    N:= 50: # for a(1)..a(N)
P3:= [0,seq(ithprime(i)^3,i=1..N+3)]:
S:= ListTools:-PartialSums(P3):
seq(S[i+4]-S[i],i=1..N); # Robert Israel, Jan 01 2024
  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[40]]^3,4,1] (* Harvey P. Dale, Jan 06 2019 *)

Formula

a(n) = A133530(n) + A030078(n+3). - Michel Marcus, Nov 08 2013

A133527 Sum of fifth powers of four consecutive primes.

Original entry on oeis.org

20207, 181226, 552276, 1969008, 4428300, 10703592, 30843448, 58052742, 124920600, 234340458, 360837752, 561553608, 910405144, 1509473242, 2207061100, 3327841200, 4713875058, 6072022352, 8304482450, 10893397986
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=20207 because 2^5+3^5+5^5+7^5=20207.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133528.

Programs

  • Mathematica
    a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]

Formula

a(n) = A133532(n) + A050997(n+3). - Michel Marcus, Nov 08 2013

A133531 Sum of fourth powers of three consecutive primes.

Original entry on oeis.org

722, 3107, 17667, 45603, 126723, 242403, 493683, 1117443, 1910643, 3504963, 5623443, 8118723, 11124243, 16188963, 24887523, 33853683, 46114323, 59408643, 73961043, 92760003, 114806643, 149150643, 198729843, 255331923, 305140563
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=722 because 2^4+3^4+5^4=722.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133532, A133533.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]

Formula

a(n) = A133535(n) + A030514(n+2). - Michel Marcus, Nov 09 2013

A133532 Sum of fifth powers of three consecutive primes.

Original entry on oeis.org

3400, 20175, 180983, 549151, 1952201, 4267249, 10332299, 29423591, 55576643, 118484257, 213829309, 332208601, 492209651, 794548943, 1362464799, 1977716093, 2909645707, 3998950759, 5227426051, 6954357343, 9089168635
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=3400 because 2^5+3^5+5^5=3400.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133533.

Programs

  • Mathematica
    a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total[#^5]&/@Partition[Prime[Range[30]],3,1] (* Harvey P. Dale, May 26 2011 *)

Formula

a(n) = A133536(n) + A050997(n+2). - Michel Marcus, Nov 09 2013

A133538 Sum of seventh powers of two consecutive primes.

Original entry on oeis.org

2315, 80312, 901668, 20310714, 82235688, 473087190, 1304210412, 4298697186, 20654701756, 44762490420, 122444491244, 289686151014, 466572884988, 778441731570, 1681334260300, 3663362624656, 5631394320840, 9203454441344, 15155831763714, 20142518677488
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=2315 because 2^7 + 3^7 = 2315.

Links

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133535, A133536, A133537.

Programs

  • Magma
    [NthPrime(n)^7 + NthPrime(n+1)^7: n in [1..25]]; // Vincenzo Librandi, Aug 23 2018
  • Maple
    seq(add(ithprime(n+k)^7,k=0..1),n=1..20); # Muniru A Asiru, Aug 22 2018
  • Mathematica
    e = 7; Table[Prime[n]^e + Prime[n + 1]^e, {n, 1, 100}]
Total/@Partition[Prime[Range[20]]^7,2,1] (* Harvey P. Dale, Oct 16 2014 *)
  • PARI
    a(n) = prime(n)^7 + prime(n+1)^7; \\ Michel Marcus, Aug 22 2018

Formula

a(n) = A092759(n) + A092759(n+1). - Michel Marcus, Nov 09 2013

A133534 Sum of third powers of two consecutive primes.

Original entry on oeis.org

35, 152, 468, 1674, 3528, 7110, 11772, 19026, 36556, 54180, 80444, 119574, 148428, 183330, 252700, 354256, 432360, 527744, 658674, 746928, 882056, 1064826, 1276756, 1617642, 1942974, 2123028, 2317770, 2520072, 2737926, 3491280
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=35 because 2^3+3^3=35.

Links

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133535, A133536, A133537, A133538.

Programs

  • Mathematica
    a = 3; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
Total[#^3]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 29 2021 *)

Formula

a(n) = A030078(n) + A030078(n+1). - Michel Marcus, Nov 09 2013

A133535 Sum of fourth powers of two consecutive primes.

Original entry on oeis.org

97, 706, 3026, 17042, 43202, 112082, 213842, 410162, 987122, 1630802, 2797682, 4699922, 6244562, 8298482, 12770162, 20007842, 25963202, 33996962, 45562802, 53809922, 67348322, 86408402, 110200562, 151271522, 192589682, 216611282
Offset: 1

Views

Author

Artur Jasinski, Sep 14 2007

Keywords

Examples

			a(1)=2^4+3^4=97.

Crossrefs

Cf. A034963, A133524, A133525, A133526, A133527, A133528, A133529, A133530, A133531, A133532, A069484, A133534, A133536, A133537, A133538.

Programs

  • Mathematica
    a = 4; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]

Formula

a(n) = A030514(n) + A030514(n+1). - Michel Marcus, Nov 09 2013
Showing 1-10 of 18 results. Next

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